ACTIVE YEAST: In a large mixing bowl, combine the warm water, sugar, and yeast. Stir gently and let it sit for about 5-10 minutes until the mixture becomes foamy.
MAKE THE DOUGH: Add the flour, 1/4 cup olive oil, and salt to the yeast mixture. Mix until a soft dough forms. Use a wooden spoon or your hands to combine the ingredients.
KNEAD THE DOUGH: Transfer the dough to a lightly floured surface and knead for about 5 minutes until it becomes smooth and elastic.
FIRST RISE: Place the kneaded dough in a lightly oiled bowl, cover it with a damp cloth or plastic wrap, and let it rise in a warm place for about 1 hour, or until it doubles in size.
PREPARE THE BAKING SHEET: Line a 9x13 inch baking sheet with parchment paper and drizzle olive oil generously over it, ensuring the entire surface is coated to prevent sticking and create a crispy crust.
SHAPE THE DOUGH: Once the dough has risen, punch it down to release air bubbles. Turn it out onto the prepared baking sheet and gently stretch and press it into a rectangle or the shape of the sheet, about 1/2 inch thick.
SECOND RISE: Cover the dough lightly with a cloth and let it rest for another 20-30 minutes.
PREHEAT THE OVEN: Preheat your oven to 400°F (200°C).
ADD TOPPINGS: Using your fingers, create dimples all over the dough's surface. Drizzle with additional olive oil and sprinkle with fresh rosemary, halved cherry tomatoes, and coarse sea salt.
BAKE THE FOCACCIA: Place the baking sheet in the preheated oven and bake for 20-25 minutes, or until the focaccia is golden brown.
COOL AND SERVE: Remove from the oven and allow to cool slightly. Cut into squares or strips and serve warm or at room temperature.